Download App

Correlation — Economics STD 11 Commerce — Question

CBSE BoardEnglish MediumSTD 11 CommerceEconomicsCorrelation6 Marks
Question
Calculate the correlation coefficient between X and Y and comment on their relationship.
X
 1
3
4
5
7
8
Y
2
6
8
10
14
16
✓

Answer

$X$
$Y$
$XY$
$X^2$
$Y^2$
1
2
2
1
4
3
6
18
9
36
4
8
32
16
64
5
10
50
25
100
7
14
98
49
196
8
16
128
64
256
$\sum\text{X}=8$
$\sum\text{Y}=56$
$\sum\text{XY}=328$
$\sum\text{X}^2=164$
$\sum\text{Y}^2=656$
$\text{r}=\frac{\sum\text{XY}-\frac{\big(\sum\text{X}\big)\big(\sum\text{Y}\big)}{\text{N}}}{\sqrt{\sum\text{X}^2-\frac{\big(\sum\text{X}^2\big)}{\text{N}}}\sqrt{\sum\text{Y}^2-\frac{\big(\sum\text{Y}\big)^2}{\text{N}}}}$
$=\frac{328-\frac{28\times56}{6}}{\sqrt{164-\frac{(28)^2}{6}}\sqrt{656-\frac{(56)^2}{6}}}$
$=\frac{328-\frac{1568}{6}}{\sqrt{164-\frac{784}{6}}\sqrt{656-\frac{3136}{6}}}$
$=\frac{328-261.33}{\sqrt{164-130.67}\sqrt{656-522.67}}$
$=\frac{66.67}{\sqrt{33.33}\sqrt{133.33}}$
$=\frac{66.67}{5.77\times11.55}$
$=\frac{66.6}{66.6}$
$=1.00$
$=1$
As the correlation coefficient between the two variables is +1, so the two variables are perfectly positive correlated.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "6 Marks Question" from Correlation→Correlation — all question types→Economics STD 11 Commerce question papers→CBSE Board STD 11 Commerce question papers→CBSE Board question paper generator→

Similar questions

Recast the following cumulative table into the form of an ordinary frequency distribution and determine value of the median.
Number of Days Absent
Number of Students
Less than 5
29
Less than 10
224
Less than 15
465
Less than 20
582
Less than 25
634
Less than 30
644
Less than 35
650
Less than 40
653
Less than 45
655
→
Define elasticity of supply. On the basis of the value of coefficient of elasticity of supply, how many types of situations can you imagine? Represent those situations diagrammatically.
→
Represent the following information through a time series graph.
Year
2005
2006
2007
2008
2009
2010
2011
Export (₹ in crore)
300
320
400
350
360
250
340
Imort (₹ in crore)
450
300
280
375
330
450
325
→
Locate the median graphically from the following data:
Marks
0-10
10-20
20-30
30-40
40-50
No. of students
10
20
30
20
10
→
Calculate the coefficient of variation of the given continuous series.
More than: 0 10 20 30 40 50 60 70
Cumulative Frequency: 100 90 75 50 20 10 5 0
Hint: Since, 'more than' distribution is givan, we first convert it into exclusive distribution.
→
Draw a Lorenz curve with the help of following data.
Weekly Wages (in ₹) Number of Workers
Factory (A) Factory (B)
6 6 2
25 11 38
60 13 52
84 14 28
105 15 38
150 17 26
170 10 12
400 14 4
→
→
Read the following hypothetical information carefully and answer the questions 1-6 on the basis of the same:
Units of LabourAverage ProductTotal ProductMarginal Product
1444
25__6
35155
4__161
5315__
1. At 2nd unit of labour employed, total product will be ____________.  (Fill up the blank with correct alternative)
(a) 7
(b) 9
(c) 10
(d) 12
 
2. At 4th unit of labour employed, average product will be ____________ .  (Fill up the blank with correct alternative)
(a) 1
(b) 4
(c) 12
(d) 64

3. Which of the following is incorrect?    (Choose the correct alternative)
(a) When marginal product decreases, total product also decreases
(b) Generally AP curve is U-shaped curve
(c) Total product can be zero or negative
(d) All of these

4. Identify the correct formula to calculate Average Product.  (Choose the correct alternative)
(a) $AP =\Sigma MP$
(b) $AP = TP _{ n }-T P_{ n -1}$
(c) $AP =\frac{ TP }{ L }$
(d) $AP =\frac{\Delta TP }{\Delta L }$

5. Read the following statements carefully and choose the correct alternative among those given below:
Statement 1 : When MP decreases, TP increases at a decreasing rate.
Statement 2 : When MP = 0, there is no addition to TP.
Alternatives:
(a) Both the statements are true
(b) Both the statements are false
(c) Statement 1 is true and Statement 2 is false
(d) Statement 2 is true and Statement 1 is false

6. At 5th unit of labour employed, marginal product will be ____________.
(Fill up the blank with correct alternative)
(a) 1
(b) -1
(c) 8
(d) 12
→
Complete the following table and also draw the market demand curve.
Price (₹)Quantity Demanded by Isha (Units)Quantity Demanded by Misha (Units)Market Demand (Units)
103-8
9-815
811-22
7-1430
62022-
→
Convert the following inclusive series into exclusive series:
C.I.
1-5
6-10
11-15
16-20
21-25
No.of Workers
10
15
20
25
30
→